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  "title": "STRAND Lab 04: Coherent Atlas & the Pairwise Impostor",
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      "arxiv_id": "2608.09958",
      "version": "v1",
      "title": "Geometrize the nongeometric space",
      "authors": ["Tran Chi Quy", "Sonnet Nguyen Quang Hung"],
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      "title": "EFT (String) Tower Building",
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      "expected_nonidentity_steps": 3,
      "expected_parenthesizations_equal": true,
      "expected_direct_match": true
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      { "id": "q2", "members": ["a2", "b1", "c0", "d2"] }
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    "expected_class_sizes": [4, 4, 4],
    "expected_all_local_points_covered": true
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      { "id": "r1a", "projections": [{ "chart_id": "chart-a", "point_id": "a1" }, { "chart_id": "chart-b", "point_id": "b0" }, { "chart_id": "chart-c", "point_id": "c2" }, { "chart_id": "chart-d", "point_id": "d0" }] },
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    ],
    "expected": {
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      "projections_per_atom": 4,
      "transition_squares_checked": 36,
      "transition_squares_commute": true,
      "quotient_fiber_sizes": [2, 2, 2]
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